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Electric potential and potential difference:

Charges can move, if there is electric potential difference across the conductor. This is done by connecting a battery or a cell in the circuit. The potential difference sets the charges in motion and produces an electric current.

Electric potential difference is defined as the work done in moving a unit positive charge from one point to another.

Note that the voltmeter is always connected in parallel across the points between which the potential difference is to be measured.

Ohm’s Law

This law states that the current (I) flowing through a conductor is directly proportional to the potential difference (V) applied across its ends, provided the temperature and other physical conditions remain unchanged.

Mathematically, V∝ I or V=RI

The proportionality constant R is called the resistance of the conductor, which is the property of a conductor to resist the flow of charges through it.

The resistance of a conductor is expressed in ohm.

Since R=V/I, 1 ohm = 1 volt/ 1 A

Factors affecting resistance of a conductor:

Resistance of a conductor depends on its length (l), its area of cross section (A) and the nature of its material, as

R ∝ l

And, R ∝ 1/A

Or, R=l/A, where is the electrical resistivity of a material and it depends on the nature of the material. Its SI unit is ohm-m.

Note that metals and alloys which are good conductors of electricity have very small value of resistivity.

Series and parallel combinations of resistors:

If in a circuit we have more than 1 resistors, they can be connected in different ways. The resultant resistance is also, therefore, different. Let us study these one by one.

Series combination of Resistors – When two or more resistors are joined end to end, they are said to be connected in series. You can now see this arrangement below.

In a series combination of resistors, same current passes through each resistor.

Whereas, the total potential difference across a combination of resistors in series is equal to the sum of potential difference across the individual resistors.

V=V1+V2+V3+…….

We know that V=IR

Therefore,

IR=IR1+IR2+IR3+……

R=R1+R2+R3+………

Parallel combination of resistors – If two or more resistors are connected together between any two points, then the resistors are said to be connected in parallel.

Let us now see total resistance in this case.

In parallel combination of resistors, potential difference across different resistors is same whereas current is different and total current through the circuit is given as –

I=I1+I2+I3+….

Therefore, net resistance is given as –

1/R=1/R1+1/R2+1/R3+…….

Heating effect of electric current and its applications

Joule’s Law of Heating

The law states that heat produced in a resistor is –

Directly proportional to the square of current for a given resistance (I2),

Directly proportional to resistance for a given current (R), and

Directly proportional to the time for which the current flows through the resistor (T).

Mathematically, H=(I^2)RT=VIT=(V^2)T/R

The generation of heat in an electric circuit can be both useful and harmful.

to produce light, as in an electric bulb. Note that a strong metal with high melting point such as tungsten (melting point 3380°C) is used for making bulb filaments, so that it does not melt at high temperatures.

Fuse used in the electric circuits – Fuse is the wire placed in series with any electrical appliance in an electric circuit, it saves the appliance from being damaged if the current exceeds the maximum safe value. If the current exceeds the maximum allowable value, then the fuse wire melts and breaks the circuit.

Electric Power:

It is the rate of consumption of energy.

When a current I flows through a circuit for a time t at a constant potential difference V, then the work done is,

W=VIt Joule

∴Electric power, P= W/t=VIt/t

VI=(I^2) R=(V^2)/R

The SI unit of power is watt.

The commercial unit of electric energy is kilowatt hour (kWh). In our electricity bills, 1 kWh is taken as one unit.